Is not a religious test as far as it is necessary, or would
operate, involved in the oath itself? If the person swearing
believes in the supreme Being who is invoked, and in the
penal consequences of offending him, either in this or a
future world or both, he will be under the same restraint
from perjury as if he had previously subscribed a test requiring
this belief. If the person in question be an unbeliever
in these points and would notwithstanding take the
oath, a previous test could have no effect. He would subscribe
it as he would take the oath, without any principle
that could be affected by either.

The Papers of James Madison. Edited by William T. Hutchinson et al. Chicago and London: University of Chicago Press, 1962--77 (vols. 1--10); Charlottesville: University Press of Virginia, 1977--(vols. 11--).